USC Predict COVID Project: Predictive Epidemic Model for COVID-19 in Los Angeles County
Abigail Horn, PhD1, David Conti, PhD
5/15/2020
Updated with data available as of 2020-05-20
Aims
The USC Predict COVID project is using an epidemic model to estimate the impact of COVID-19 in Los Angeles County
* We are addressing the key questions of:
- When will the peak of the epidemic occur and how will it impact health care capacity?
- What happens to the dynamics of the epidemic when social distancing ends?
- How will the epidemic affect different at-risk groups?
* Critical healthcare variables predicted by the model are the counts of the numbers of individuals over time, including the peak occurrence, for the following:
- The total number of infected cases including both the number detected and observed with testing and the undetected/untested cases
- The total number of individuals hospitalized (including those in the ICU)
- The number of patients in the ICU
- The number of patients on ventilators
- The number of deaths
* We estimate a number of key epidemic parameters, including:
- \(R0\), the reproductive number or average number of new infections generated by an infected person in a completely susceptible population
- \(r\), the proportion of illnesses that are detected and reported out of all illnesses. In this document we will consider that a prior for \(r\) can be directly informed by seroprevalence studies.
- \(Frac_{R0}\), the factor reduction in the initial R0 due to social distancing
- \(Pr(Hospital | Illness)\), the probability of hospitalization given illness
- \(Pr(Ventilation | ICU)\), the probability of ICU care necessary given hospitalization
- \(p_v\), the probability of ventilation given ICU care
- \(Pr(Death | ICU)\), the probability of death given ICU care
* We provide projections of illness severity trajectories in L.A. County as a whole and for race/ethnicity groups, based on prevalence of known COVID-19 risk factors.
(1) Model projections
(1.1) Projections Against Data
Demonstrating model fit against COVID-19 data for Los Angeles, for the following variables/compartments:
- New = new daily incidence
- Current = current census in compartment
- Cumulative = running total over time
COVID-19 data is shown as black dots in the figures below.
Short time horizon
Longer time horizon
{-}
(1.2) Detailed Projections by Key Compartments
Projections for key compartments:
- Current census in Hosptial
- Current census in ICU
- Current census in Ventilation
- Cumulative deaths
- Current Illnesses: Observed
- Current Illnesses: Total (observed + unobserved)
Current in Hospital
Current in ICU
Current in Ventilation
Cumulative Deaths
Current Observed Illnesses
Current Total Illnesses (Observed + Unobserved)
{-}(1.3) Projections for LA County and by SPA Given Risk Factors
Risk Profiles, Risk Factors, and Risk Groups
- The following table presents the model-estimated probabilities \(Pr(Hospital | Illness,Profile_i)\), \(Pr(ICU | Hospital,Profile_i)\), and \(Pr(Death | ICU,Profile_i)\) for each risk group (or combination of risk factors), as well as the prevalence of these risk groups/factors in the general L.A. County Population \(Pr(Profile_i)\).
Projections by Risk Factors
- These figures show the estimated proportion of each risk group that will make up the resulting cohorts of COVID patients admitted to hospital, admitted to ICU, or that die within the L.A. County/SPA population, based on the population prevalence of the risk group in L.A. County/SPAs.
- The analyses are presented for each risk group, as well as stratified to the individual risk factors (age, comorbidities, obesity status, smoking status).
By SPA, stage of disease
By stage of disease, SPA
Comparing risk factors
Age by stage of disease
Comorbidity by stage of disease
BMI by stage of disease
Smoking by stage of disease
Projections across risk factors: Fraction of all LA County Cases by risk factor
By risk group
By age
By comorbidity
By obesity status
By smoking status
(1.4) Projections by Race / Ethnicity
Projections by race/ethnicity
- These figures show the estimated proportion of each risk group that will make up the resulting cohorts of COVID patients admitted to hospital, admitted to ICU, or that die within each race/ethnicity population, based on the population prevalence of the risk group in race/ethnicity groups.
- The analyses are presented for each risk group, as well as stratified to the individual risk factors (age, comorbidities, obesity status, smoking status).
Risk groups by stage of disease, race
Risk groups by race, stage of disease
Age by stage of disease, race
Comorbidity by stage of disease, race
BMI by stage of disease, race
Smoking by stage of disease, race
Projections across race/ethnicity: Fraction of all LA County Cases by Race
- Due to disparities in the prevalence of health conditions, health behaviors, and age – the risk factors for COVID-19 – the relative risk of death is not distributed equally across each race/ethnicity.
- These figures demostrate the projections of the relative share of hospitalizations, ICU admissions, and deaths by race/ethnicity from our model, which accounts for biological COVID-19 risk factors. Values are compared with the baseline distribution of the relative share of the L.A. County population in each race/ethnicity group.
Deaths by race: Model projections vs. observed LA data
- This figure compares the projections of the relative share of deaths by race/ethnicity from our model with the observed relative share of deaths by race/ethnicity in L.A. County. The population prevalence of each race/ethnicity is also provided as a baseline (left column).
- A key insight from this figure is that as the epidemic evolves, the trend in death rate by race/ethnicity appears to be converging to the biological expected risk as calculated by our model.
- Only time will tell if this stabilies or if the death rate by race/ethnicity grows disproportionately to that expected by biological factors alone as the epidemic progresses.
Projected illness severity by race
Projected illness trajectories by race and risk group
Summary
- Predictive epidemic modeling can help to evaluate the public health strategies for limiting the spread of COVID-19. LA County is succeeding in mitigating the epidemic curve due to strong adherence to social distancing (model-estimated reduction in contact rate of >70%).
- Our model suggests that social distancing may need to be continued for a longer period of time to retain these mitigation effects.
- Our model predicts that higher risk groups – characterized not only by advanced age but also combinations of existing health conditions – will make up the majority of those afflicted with severe disease. We analyze how these risk factors project onto race/ethnicity groups and project expected illness patterns based on population size and prevalence of these risk factors.
- Model estimates can and will change as new studies and data become available.
(3) Methods and data
(3.1) Model overview
Why our model is unique
- Our epidemic compartmental model uses stochastic differential equations and approximate Bayes calculation techniques for parameter estimation.
- Importantly, the model presents the uncertainty in all estimations and predictions.
- We incorporate prior information for parameter specification.
- We incorporate risk factors (e.g. advanced age, existing health conditions) into the analysis.
- We can modify parameters at different time points, enabling the specification of interventions, e.g. social distancing scenarios
Stochastic epidemic model:
- Deterministic model: for given values of parameters, dynamics across compartments will be fixed.
- Stochastic model: Appropriate probability distributions are used model the transfer of individuals across compartments.
What a stochastic model allows:
- Looking back: Provides a better framework for parameter estimation, based on observed data
- Looking forward: Enables forecasts with confidence bounds that account for variability in parameters
Approximate Bayesian Computation (ABC) for parameter estimation:
- Allows us to incorporate the uncertainty in all the parameters in fitting the model to data and estimating parameters
- Allows us to include all prior information and/or assumptions about the distribution (the range of values) for each parameter
- Allows us to prioritize data input that is more reliable in fitting the model to data (e.g., not including more unreliable early illness count data)
(3.2) Stochastic differential equation epidemic model
Flow diagram
Compartmental model flow diagram
System of Equations
\[ \begin{align*} dS/dt &= -\beta S(I+A)\\ dE/dt &= \beta S(I+A) - \tfrac{1}{d_{EI}}E\\ dA/dt &= \tfrac{1-r}{d_{EI}}E - \tfrac{1}{d_{IR}}A\\ dI/dt &= \tfrac{r}{d_{EI}}E - (\tfrac{\alpha}{d_{IH}}\tfrac{1-\alpha}{d_{IR}})I\\ dH/dt &= \alpha (\tfrac{\alpha}{d_{IH}}\tfrac{1-\alpha}{d_{IR}})I - (\tfrac{\kappa}{d_{HQ}}\tfrac{1-\kappa}{d_{HR}})H \\ dQ/dt &= \kappa (\tfrac{\kappa}{d_{HQ}}\tfrac{1-\kappa}{d_{HR}})H - (\tfrac{\delta}{d_{QD}}\tfrac{1-\delta}{d_{QR}})Q \\ dV/dt &= p_V Q\\ dD/dt &= \delta (\tfrac{\delta}{d_{QD}}\tfrac{1-\delta}{d_{QR}})Q\\ dR/dt &= (1-\alpha) (\tfrac{\alpha}{d_{IH}}\tfrac{1-\alpha}{d_{IR}})I + (1-\kappa) (\tfrac{\kappa}{d_{HQ}}\tfrac{1-\kappa}{d_{HR}})H + (1-\delta)(\tfrac{\delta}{d_{QD}}\tfrac{1-\delta}{d_{QR}})Q + \tfrac{1}{d_{IR}}A \ \end{align*} \]
\[ R0 = \beta ({\frac{r}{\tfrac{\alpha}{d_{IH}}+\tfrac{1-\alpha}{d_{IR}}}+ (1-r){d_{IR}}}) \\ N=S+E+A+I+H+Q+D+R \]
Model parameters
| Parameter | Description | Value |
|---|---|---|
| \(R0\) | Basic reproductive number | Estimated |
| \(\beta\) | transmission rate | Analytically derived from model and R0 |
| \(d_{EI}\) | days between exposure and infectivity (incubation period) | 5 days |
| \(d_{IH}\) | days between symptom onset and hospitalization (if required) | 10 days |
| \(d_{IR}\) | days between symptom onset and recovery (if not hospitalized) | 7 days |
| \(d_{HQ}\) | days between hospitalization and ICU (if required) | 1 days |
| \(d_{QR}\) | days between hospitalization and recovery (if ICU not required) | 12 days |
| \(d_{QD}\) | days between ICU and fatality | 8 days |
| \(d_{QR}\) | days between ICU and recovery | 7 days |
| \(\alpha\) | probability infected (I) requires hospitalization (vs. recovers) | Estimated |
| \(\kappa\) | probability hospitalized (H) requires ICU (vs. recovers) | Estimated |
| \(\delta\) | probability ICU (Q) patient dies | Estimated |
| \(p_V\) | probability ventilation (V) required given ICU | Estimated |
| \(N\) | Total population size | |
| \(S\) | Susceptible population | |
| \(E\) | Exposed not yet infectious | |
| \(A\) | Infected, unobserved | |
| \(I\) | Infected, observed | |
| \(H\) | In Hospital | |
| \(Q\) | In ICU | |
| \(V\) | On ventilator | |
| \(D\) | Dead | |
| \(R\) | Recovered/removed |
Model parameters - fixed, taken from literature: - Transition times between compartments - Sources provided at this link
Model Parameters — estimated by our model - \(R0\), the reproductive number or average number of new infections generated by an infected person in a completely susceptible population - \(r\), the proportion of illnesses that are observed - \(Frac_{R0}\), the reduction in the initial R0 due to social distancing - \(\alpha\), the probability of hospitalization given illness, i.e. \(Pr(Hospital | Illness)\) - \(\kappa\), the probability of ICU care necessary given hospitalization, i.e. \(Pr(ICU | Hospital)\) - \(p_v\), the probability of ventilation given ICU care, i.e. \(Pr(Ventilation | ICU)\) - \(\delta\), the probability of death given ICU care, i.e. \(Pr(Death | ICU)\)
(3.3) Prior parameter specifications
Model estimated parameters: Prior information and posterior estimates Here we summarize our estimated parameter values for key epidemic and model quantities:
- \(R0\), the reproductive number or average number of new infections generated by an infected person in a completely susceptible population
- \(r\), the proportion of illnesses that are observed
- \(Frac_{R0}\), the reduction in the initial R0 due to social distancing
- \(Pr(Hospital | Illness)\), the probability of hospitalization given illness
- \(Pr(ICU | Hospital)\), the probability of ICU care necessary given hospitalization
- \(Pr(Ventilation | ICU)\), the probability of ventilation given ICU care
- \(Pr(Death | ICU)\), the probability of death given ICU care
Because our model is stochastic and we are using Bayesian techniques for parameter estimation, each posterior parameter estimate is represented by a distribution of likely values.
Summary of key estimated parameters
Summary of key statistics of each estimated parameter: the mean and the standard deviation (sd).
| R0 | Prop. cases detected (r) | Frac R0 Mar11 | Pr(Death|ICU) | Pr(Hospital|Illness) | Pr(ICU|Hospital) | Pr(Ventilation|ICU) | |
|---|---|---|---|---|---|---|---|
| mean | 3.8687 | 0.0283 | 0.2394 | 0.6247 | 0.3194 | 0.3889 | 0.4822 |
| sd | 0.1002 | 0.0054 | 0.0549 | 0.1131 | 0.1499 | 0.0969 | 0.0484 |
Prior on illness severity probabilities \(Pr(Hospital | Illness)\), \(Pr(ICU | Hospital)\), \(Pr(Death | ICU)\): Risk modeling and previous COVID-19 studies
We use previous studies to narrow the specification of the probability of hospitalization given illness, admittance to the intensive care unit (ICU) given being in hospital, ventilation given being in ICU, and death given being in ICU by incorporating risk factors, including age, sex, smoking and other comorbidities. The prevalence of these risk factors in Los Angeles County is also included.
The comorbidities included in the “any comorbidity” category are: hypertension, diabetes, cardiovascular disease, cerebrovascular disease / stroke, cancer, COPD, and athsma. It is important to note that each of these conditions has its own risk of disease outcome; future models will disaggregate risk estimates by specific risk conditions when sufficient data becomes available to produce these estimations.
(1) Estimating the conditional probability of COVID illness severity given combinations of risk factors
- Using studies reporting the marginal risk of severe COVID-19 outcomes given individual risk factors, we develop a statistical model to estimate the probability of COVID illness trajectories for individuals with combinations of risk factors.
- Specifically, we estimate the probability that individuals having (or not) combinations of risk factors are admitted to hospital given having acquired illness \(Pr(Hospital | Illness)\), are admitted to the ICU given admittance to hospitalized \(Pr(ICU | Hospital)\), and that die given being admitted to the ICU \(Pr(Death | ICU)\).
- Our methodology for joint risk factor estimation relies on a model, called JAM, developed for use in genome-wide analyses to identify the conditional relative risk (RR) of phenotypic occurrence given joint combinations of genes from two pieces of information: (i) the marginal RR between single genes and phenotype and (ii) the correlation structure between the genes.
- We apply the JAM model to estimate the conditional RR of COVID-19 illness severity (hospitalization, ICU, and death) given joint combinations of risk factors. For information informing (i) we obtain the marginal RR between individual risk factors and COVID-19 illness severity from published COVID-19 studies (sources below, peer-reviewed where available). For (2), we obtain the correlation structure between the risk factors using data from The National Health and Nutrition Examination Survey (NHANES). NHANES is a survey research program conducted by the National Center for Health Statistics (NCHS) to assess the health and nutritional status of adults and children in the United States, and to track changes over time. We use the NHANES cohort of 2017-2018.
- After obtaining the conditional RR of COVID-19 illness severity (hospitalization, ICU, and death) given joint combinations of risk factors, we convert these to the probabilities \(Pr(Hospital | Illness, Profile_i)\), \(Pr(ICU | Hospital,Profile_i)\), and \(Pr(Death | ICU,Profile_i)\).
- The analysis we present here has taken the combinations of risk factors and grouped these into 5 key risk groups according to similar within-group levels of the probabilities \(Pr(Hospital | Illness, Profile_i)\), \(Pr(ICU | Hospital, Profile_i)\), and \(Pr(Death | ICU, Profile_i)\).
- To produce an estimate of the overall \(Pr(Hospital | Illness)\) across all risk groups for L.A. County and subpopulations, we take the weighted average of the probability for each risk group and the prevalence of the risk group in all illnesses, i.e.
\[ \begin{align*} Pr(Hospital | Illness) = \sum_i Pr(Group_i | Illness)Pr(Hospital|Group_i,Illness) \end{align*} \] We assume that the prevalence of the risk group in the ill population, \(Pr(Group_i|Illness)\), is equal to the prevalence of the group in the general population of L.A. County, i.e. \(Pr(Group_i)\). We again borrow the correlation structure between risk factors derived from the NHANES cohort to estimate the population prevalence \(Pr(Group_i)\) from available data on the prevalence of individual risk factors.
The same approach is applied to estimate \(Pr(ICU | Hospital)\) and \(Pr(Death|ICU)\): \[ \begin{align*} Pr(ICU | Hosptial) = \sum_i Pr(Group_i | Hospital)Pr(ICU|Group_i,Hospital)\\ Pr(Death | ICU) = \sum_i Pr(Group_i | ICU)Pr(Death|Group_i,ICU) \end{align*} \]
(2) Estimating the proportion of each risk group that will make up the cohorts of COVID patients admitted to hospital, admitted to ICU, or that die in L.A. County and SPAs
- We estimate the proportion of each risk group that will make up the cohorts of COVID patients admitted to hospital (\(Pr(Group_i|Hospital\))), admitted to ICU (\(Pr(Group_i|ICU\))), or death (\(Pr(Group_i|Death\))) in L.A. County population and each SPA, as the relative share of each group and disease status, i.e. \[ \begin{align*} Pr(Group_i|Hospital) = \frac{Pr(Group_i|Illness)Pr(Hospital|Group_i,Illness)}{Pr(Hospital|Illness)}\\ Pr(Group_i|ICU) = \frac{Pr(Group_i|Hospital)Pr(ICU|Group_i,Hospital)}{Pr(ICU|Hospital)}\\ Pr(Group_i|Death) = \frac{Pr(Group_i|ICU)Pr(Death|Group_i,ICU)}{Pr(Death|ICU)}\\ \end{align*} \] We multiply the group prevalences above by the trajectory median values for number in hospital, ICU, and death from the epidemic model to arrive at the trajectory breakdowns presented above.
Data sources
COVID-19 Illness Trajectory Relative Risks
Studies on COVID-19 clinical presentation and trajectories to inform the probability of hospitalization, ICU, and ventilation based on single risk factors:
- Guan, Wei-jie, et al. “Clinical characteristics of coronavirus disease 2019 in China.” New England Journal of Medicine (2020).
- Petrilli, Christopher M., et al. “Factors associated with hospitalization and critical illness among 4,103 patients with COVID-19 disease in New York City.” medRxiv (2020).
- Summary table of the modified Relative Risks (RR) coming from these studies, which are used by our statistical model estimates
L.A. County Risk Factor Prevalences - Los Angeles County Health Survey - UCLA California Health Information Survey
Prior on \(R0\), Reproductive number: Previous COVID-19 studies
- Mean = 3.869
Standard deviation = 0.1
\(R0\) prior estimate is based on values for \(R0\) estimated from other published studies on COVID-19.
Prior and posterior 
Prior on \(r\), fraction of illnesses that are observed: Seroprevalence studies
- Mean = 0.028
Standard deviation = 0.005
- A seroprevalence study conducted on the Los Angeles on April 10-11, 2020, by Neeraj Sood and LADPH, found the prevalence of antibodies in 3.6% (1.7,5.2) of the sampled population.
We use this information to inform two pieces of information: (i) the prior distribution for \(r\), the fraction of observed illnesses over all illnesses, and (ii) an observed data point for the number of counts in the Recovered compartment. We make the following assumptions:
Prior distribution for \(r\) - The seroprevalence study retuns an estimated % of the population of L.A. that has antibodies for COVID-19 by the study date. We assume this is equal to the proportion of total recovered individuals as of a week prior to the study date, April 4, 2020, since it takes a week for antibodies to develop. - Meanwhile, we assume the fraction of observed illnesses \(r\) is approximately equal to the fraction of recovered cases as:
\[ \begin{align*} \mathbf{r} = \frac{cum. obs. I(t = t')}{cum. tot. I(t=t')}\\ \approx \frac{cum. obs. R(t=t')}{cum.tot.R(t=t')}\\ \end{align*} \] - The seroprevalence study informs the denominator, the total recovered cases at \(t'\) = April 4. - The numerator, the “observed” recovered cases at time \(t'\), is assumed to be approximately equal to the observed illnesses at time \(t'-\) [1,3] weeks, which is the assumed period from infectiousness to recovery. - We specify the minimum and maximum values for the prior for \(r\) \(Pr(r)\) using the equation above with the range of the % of the population with antibodies on of April 4, and the number of observed illnesses 1-3 weeks prior to that. - In addition to using the seroprevalence study to inform the prior distribution on \(r\), we use it to inform the
Data point on number in Recovered compartment
We use the results of the seroprevalence study to inform a fixed data point representing the number of counts in the Recovered compartment on April 4. We use this data point together with the approximated timing of the first recovered case (1-3 weeks after the start date of the outbreak) to interpolate an exponential distribution in the time series of counts in the Recovered compartment. This is then used as an observed data input alongside the other observed compartment variables (illnesses, hospitalizations, deaths, etc.) in the parameter estimation procedure.
These estimates will be greatly improved by time series of COVID-19 seroprevalence, i.e. as results of future seroprevalence studies become available.
Prior and posterior 
Prior on \(Frac_{R0}\), the reduction in the initial R0 due to social distancing: Mobility data
- Mean = 0.239
Standard deviation = 0.055
We use mobility data to narrow the specification of the reduction in the average number of new infections due to an infected person (R0) in a completely susceptible population under recent social distancing restrictions.
Effectively, reductions in mobility correspond to a proportional reduction in R0
- Reduction in mobility observed in LA County:
Mobility reduction
and
encounter reduction
Source: Assessing changes in commuting and individual mobility in major metropolitan areas in the United States during the COVID-19 outbreak and Unacast COVID-19 Social Distancing Scoreboard
- Our modeled reduction in R0 timeline:
Prior and posterior 
Joint posterior densities of interest
(3.4) Projections by Key Risk Groups and Risk Factors
We extend the risk factor analysis above to estimate the proportion of each risk group that will make up the cohorts of COVID patients admitted to hospital, admitted to ICU, or that die in L.A. County, across the SPAs, and across the race/ethnicity groups
Estimating the conditional probability of COVID illness severity given combinations of risk factors
- We estimate the proportion of each risk group that will make up the cohorts of COVID patients admitted to hospital (\(Pr(Group_i|Hospital\))), admitted to ICU (\(Pr(Group_i|ICU\))), or death (\(Pr(Group_i|Death\))) in L.A. County population and each SPA, as the relative share of each group and disease status, i.e. \[ \begin{align*} Pr(Group_i|Hospital) = \frac{Pr(Group_i|Illness)Pr(Hospital|Group_i,Illness)}{Pr(Hospital|Illness)}\\ Pr(Group_i|ICU) = \frac{Pr(Group_i|Hospital)Pr(ICU|Group_i,Hospital)}{Pr(ICU|Hospital)}\\ Pr(Group_i|Death) = \frac{Pr(Group_i|ICU)Pr(Death|Group_i,ICU)}{Pr(Death|ICU)}\\ \end{align*} \] We multiply the group prevalences above by the trajectory median values for number in hospital, ICU, and death from the epidemic model to arrive at the trajectory breakdowns presented above.
(3.5) Data
Illness case data
- We use current numbers of infected (observed), hospitalized, ICU, ventilated, and deaths, as well as the capacity (total number of resouces available) at hospitals, ICUs, and ventilators in L.A. County from the Los Angeles County Department of Public Health, updated daily by Faith Washburn (shared privately)
- The data used in this version of the report includes counts up through 2020-05-20
Data processing: Skilled Nursing Facility (SNF) counts removed from LA County daily counts
- We are fitting our model to the general COVID-19 illness trends in L.A. County. Due to the large number of outbreaks and the share of deaths coming from nursing homes (Skilled Nursing Facilities, SNFs), we have removed estimated numbers of illnesses, hospitalizations, ICU visits, ventilations, and deaths from SNFs. We fit our general population model to the data with the SNF cases removed, as illustrated below.
- Counts removed from Illnesses, Hospitalizations, Ventilations, and Deaths
(3.6) Model Limitations
- This model does not account for differences in contact patterns within and across key groups, such as workplaces, schools, and communities; or of group-specific social distancing scenarios.
- This model does not account for the role of interventions beyond social distancing, such as contact tracing and surveillance testing, which are critical to identifying and limiting the spread of the virus.
- This model focuses only on the direct effects of stay-at-home orders on COVID-19 infection transmission and hospitalization. It does not account for the non-COVID-19 related public health impact of stay-at-home orders.
- This model does not account for unanticipated behavioral responses to the effects of interventions or mitigation strategies
- The accuracy of the parameter estimation depends on the accuracy of the prior specifications and any fixed parameters employed, including the incubation and recovery period. As new information about the epidemiological characteristics of COVID-19 continues to arise, model estimation will need to be continuously updated.
- Incorporating the latest information into our models is possible and will be key to maintaining its relevance for decision insights.
Acknowledgements
- We would like to acknowledge Claire Jacquillat and Adam Taylor for their contributions related to data wrangling, cleaning, interpretation, and visualization.
(2) Social distancing scenarios
SCENARIOS EVALUATED: Increase contact rate on May 16th, 2020 by variable amounts
Scenarios evaluated
7 are illustrated here. Each scenario corresponds to a different amount of contact rate, and can be understood in terms of:
Maintain current level of social distancing
Equal to:
% of original R0: 36.7
Equal to:
% of original R0: 49.3
Equal to:
% of original R0: 62
Equal to:
% of original R0: 74.7
Equal to:
% of original R0: 87.3
Equal to:
% of original R0: 100
Equal to: